High-resolution probabilistic estimation of three-dimensional regional ocean dynamics from sparse surface observations

Niloofar Asefi; Tianning Wu; Ruoying He; Ashesh Chattopadhyay

physics.ao-phApr 3, 2026

High-resolution probabilistic estimation of three-dimensional regional ocean dynamics from sparse surface observations

Authors: Niloofar Asefi, Tianning Wu, Ruoying He, Ashesh Chattopadhyay

Organizations: Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA 95064, USA · Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, NC 27695, USA · Department of Applied Mathematics, University of California, Santa Cruz, CA 95064, USA

Abstract

The ocean interior regulates Earth's climate but remains sparsely observed due to limited in situ measurements, while satellite observations are restricted to the surface. We present a depth-aware generative framework for reconstructing high-resolution three-dimensional ocean states from extremely sparse surface data. Our approach employs a conditional denoising diffusion probabilistic model (DDPM) trained on sea surface height and temperature observations with up to 99.9 percent sparsity, without reliance on a background dynamical model. By incorporating continuous depth embeddings, the model learns a unified vertical representation of the ocean states and generalizes to previously unseen depths. Applied to the Gulf of Mexico, the framework accurately reconstructs subsurface temperature, salinity, and velocity fields across multiple depths. Evaluations using statistical metrics, spectral analysis, and heat transport diagnostics demonstrate recovery of both large-scale circulation and multiscale variability. These results establish generative diffusion models as a scalable approach for probabilistic ocean reconstruction in data-limited regimes, with implications for climate monitoring and forecasting.

Figures & tables

Figure 1: Schematic of the depth-aware conditional DDPM framework for three-dimensional ocean reconstruction. Sparse observations of SSH and SST are used with a log-normalized continuous depth coordinate and used as conditioning inputs to a conditional denoising diffusion probabilistic model (DDPM). A single unified model is trained across nine discrete depth levels and learns a continuous vertical representation of the ocean interior. During inference, the model reconstructs T, S, U, and V fields not only at trained depths but also at previously unseen depths within the training range, enabling vertical interpolation without memorizing discrete layers.

Figure 2: Sparse surface observations and depth-aware DDPM reconstruction of subsurface ocean variables at three depths. Panel a shows sparse satellite SSH and SST observations on February 13, 2023, which are used to reconstruct 3D ocean states in panel b. Panel b shows subsurface ocean variables, including T, S, U, and V is shown over the Gulf of Mexico at three different depths: 55 m, 318 m, and 1062 m. The DDPM reconstructions (top row) are compared with the corresponding ground-truth fields from the GLORYS reanalysis (bottom row) for each depth. Only three depths are displayed here for clarity, and reconstructions at the other depths are included in the Supplementary Material. White areas indicate land/bathymetry. As depth increases, the valid ocean domain decreases due to bathymetric constraints, resulting in a larger land mask at deeper levels.

Figure 3: Averaged Fourier power spectra for subsurface ocean variables at three depths. The power spectra of T, S, U, and V is displayed for 100 test samples at three different depths: 55 m, 318 m, and 1062 m. Power spectra from the DDPM reconstructions are compared with the corresponding GLORYS reanalysis reference across spatial wavenumbers.

Figure 4: Quantitative evaluation of reconstructed subsurface variables across depths and models. Reconstruction performance for T, S, U, and V across 100 test samples. Columns correspond to various evaluation metrics, including normalized RMSE (NRMSE), correlation coefficient (CC), and SSIM. Results are compared across three models: DDPM, UNet+DDPM, and FNO+DDPM. Rows show results at three depths: 55 m, 118 m, and 1062 m.

Figure 5: Meridional heat-flux longitude–depth transects at $26^{\circ}$ N on 13 February 2023. Longitude–depth transects of meridional heat flux for the GLORYS reanalysis dataset (Truth) and the DDPM reconstruction are shown over the longitude range $[-99^{\circ},-74^{\circ}]$ .

Figure 6: Depth-aware DDPM reconstructions at three previously unseen depths within the training vertical range. Reconstructions are shown for previously unseen depths of 34.43 m, 266 m, and 763.3 m, which were not included during training.

Figure 7: Averaged Fourier power spectra for subsurface variables at previously unseen depths. Power spectra for temperature, salinity, zonal velocity (U), and meridional velocity (V) are shown for 100 test samples at depths of 34.43 m, 266 m, and 763.3 m that were not used during training.

Conditional Diffusion Models

Conditional diffusion models generate or infer data by steering iterative denoising with observations, labels, text, physical constraints, or other inputs.

See all 277 papers

Incomplete Observations Boost Evolutionary Performance in Ocean Modeling
Jul 21, 2026Yangyang Kong, Yutong Jiang, Yanhai Gan +3Learning with Missing Data Data Assimilation
State Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao, China · School of Computer Science and Technology, Ocean University of China, Qingdao, China
OceanDepths: A Global Dataset of Paired Subsurface and Surface Ocean Observations
Aug 17, 2026Simon Donike, Ruben Cartuyvels, Antonino Ian Ferola +3
Image Processing Laboratory, University of Valencia, Av. de Blasco Ibáñez 13, 46010, Spain · ESA-ESRIN, Via Galileo Galilei 1, 00044 Frascati RM, Italy
An Adaptive Spatiotemporal Clustering Framework for 3D Ocean Subsurface Temperature Reconstruction
Apr 21, 2026Ming Shan Loo, Wengen Li, Xudong Jiang +4Clustering
School of Computer Science and Technology, Tongji University, Shanghai, China · The Key Laboratory of Road and Traffic Engineering, Ministry of Education, College of Transportation, Tongji University, Shanghai, China · Project Management Office of China National Scientific Seafloor Observatory, Tongji University, Shanghai, China

Jul 21, 2026J/K move · Enter open · S save

Incomplete Observations Boost Evolutionary Performance in Ocean Modeling

Yangyang Kong, Yutong Jiang, Yanhai Gan, Junyu Dong+2

State Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao, China · School of Computer Science and Technology, Ocean University of China, Qingdao, China

Learning with Missing Data Data Assimilation Hidden Markov Models State Space Models

Open paper AskPDF arXiv

Data-driven methods have revolutionized ocean modeling, yet current approaches rely heavily on complete reanalysis datasets, imposing computational constraints and limiting model performance to that of the training data. Here, we present a generative state-space model and an optimization framework that enable learning directly from sparse and noisy observations. The model is essentially a hidden Markov model with a continuous state space, where oceanic physical quantities are treated as hidden states and measurements as observations, enabling a unified representation of ocean fields and observational data. Both the initial-state and state-transition modules are implemented as neural networks to capture the complexity and temporal evolution of ocean states, while the emission module is formulated as a masked Gaussian distribution. To train the model from sparse observations, we derive an optimization framework based on the expectation-maximization (EM) algorithm. The framework alternately reconstructs high-fidelity ocean fields via Langevin dynamics and optimizes deep neural networks to capture temporal evolution. Theoretical analysis shows that the framework maximizes the likelihood of observations under the generative model. For efficiency, we assume that ocean-state evolution follows a stationary, ergodic, and Markovian stochastic process and adopt only length-two state sequences during optimization. Experiments on CMIP6 simulation data and FY-3D satellite data demonstrate high-fidelity reconstruction and accurate prediction, showing that sparse observations can directly improve the model's representation of ocean-state dynamics. This work offers a scalable pathway for next-generation Earth system models to learn directly from sparse, incomplete real-world observations.

Abstract

Conditional Diffusion Models

Explore similar work

Incomplete Observations Boost Evolutionary Performance in Ocean Modeling

OceanDepths: A Global Dataset of Paired Subsurface and Surface Ocean Observations

An Adaptive Spatiotemporal Clustering Framework for 3D Ocean Subsurface Temperature Reconstruction